Values of Teaching Mathematics

Values of Teaching Mathematics

The Value of Mathematics is used in each step for our life. We cannot survive without Mathematics. It gives happiness in our life when we make our career with help of Mathematics.

1.     Practical or Utilitarian Value :  Everybody uses mathematics in their daily life. Any person who is ignorant of mathematics can be easily cheated. He will always be at the mercy of others. We have to make purchases daily. We buy cloth, food items, fruit, vegetables, grocery etc. We have to calculate how much we have to pay for everything.  Mathematics is needed by everyone whether rich or poor, high or low.

2.     Intellectual values : Develops intellectual powers , imagination , Memorization ,Observation , Invention , Concentration , Originality , Creativity , reasoning . If a child faces mathematical problems, his mind become active in solving that problem.

3.     Social values : Social values can be acquired  like:  Tolerance ,Open mindedness ,Objectivity , Honesty , Truthfulness , Co-operation , Will power, Organization and maintenance of social institutions , banks , co-operations ,Railways . post offices

4.      Moral values : Ability in arguing on the correctness and incorrectness of a statement. Develops moral qualities, Honesty , Truthfulness , Justice ,Dutifulness ,Punctuality , self confidence ,  power of distinguishing between right and wrong , Cleanness , Patience ,  listening to others , respect to others Deprives off the feelings of jealousy, hate etc.

5.     Disciplinary Values : “Mathematics is the way to settle in the mind a habit of reasoning” -Locke . As mathematical knowledge is exact, logical, real and to that point, it creates discipline in a human mind. Develops an ability to grasp a situation , to analyse the situation and to perceive correctly the state of affairs .Helps the students to imbibe qualities, Simplicity,  Accuracy , Certainty of results , Originality , Similarity to reasoning in life ,Verification of results , Concentration of mind .

6.     Cultural values : “Mathematics is the mirror of civilization”  By the culture of a nation or society we mean the mode of living of its inhabitants. Helps in promoting cultural heritage an transmitting it to future generation.  The welfare of our civilization is almost depends upon scientific and mathematical developments.  Helped in the development of various subjects and occupations.

7.     International values:  Mathematicians research their mathematical ideas from one nation to another nation.  Mathematician’s books and journals are circulated among almost all the nations of the world.

8.     Aesthetic values :  “Education as a whole should foster the higher impersonal pleasures” -Thorndike One gets pleasure in solving mathematical problems, especially when he get correct answers to his problems. Different symmetric designs by Ramanujan are a source of great pleasure Eg: Mathematics is closely related with arts like drawing, painting, music etc .All musical instruments like harmonium, drum, flute, guitar, violin etc are played with the rules of mathematics.

9.     Vocational values : Mathematics has great vocational values. Study of mathematics prepares the students for a wide variety of vocations. It finds extensive application in all vocations like:  Agriculture , Accountancy , Banking , Business , Engineering , information technology , Tailoring , Carpentry . Surveying etc.

10.            Psychological values : Mathematics helps to develop positive attitudes such as open mindedness, reasoning etc. The learning of mathematics is based on fundamental principles of psychology such as learning by doing learning through experiences and problem solving etc.

Teaching of mathematics results in the development of a number of fruitful values in the students. Only a resourceful teacher of mathematics with his deliberate efforts and planning can make it possible for the students to realize these values. So we have to realise the value & product good civilian for our nation and  for the betterment of society.

Analytic Method Synthetic Method

Analytic Method Synthetic Method

Analytic Method:

It proceeds from unknown to known. ‘Analysis’ means ‘breaking up’. In this method we break up the unknown problem into simpler parts and then see how these can be recombined to find the solution. So we start with what is to be found out and then think of further steps or possibilities the may connect the unknown built the known and find out the desired result.

Procedure:

Example: If (ac- 2b²)÷ b = (c²-2bd) ÷d  prove that   a/b=c/d,

Solution start from unknown i.e. to solve this problem we have to start from

(ac- 2b²)÷ b = (c²-2bd) ÷d   after calculation

 We get the answer a/b=c/d

Example:

If a²+b²=7ab prove that 2log (a+b) = 2log3+loga+logb

Proof:

To prove this using analytic method, begin from the unknown.

The unknown is 2log (a+b) = 2log3+loga+logb

Now, 2log (a+b) = 2log 3+ log a+ log b is true

If log (a+b)² = log 3² + log a + log b is true

If log (a+b)² = log 9 + log ab is true

If log (a+b)² = log 9ab is true

If (a+b)² = 9ab is true

If a²+b²+2ab =9ab is true

Then  a²+b²=7ab which is known and true

Thus if a²+b²= 7ab  prove that 2log (a+b) = 2log3+loga+logb

Merit of Analytic Method

• It is logical method. It leaves no doubts and convinces the learner.
• It helps student in understanding and strengthen the urge to discover facts.
• Each steps has the  its reason and justification. So, no fixed steps is required.

·         It is a method of discovery.

·          It is a process of thinking (exploration).

·          It pulls apart or breaks up the statement under solution.

·         It answers satisfactorily and question that may arise in the mind of pupil.

·          The students can recall and reconstruct easily any step if forgotten.

·          It develops originality.

Demerit of Analytic Method

·         It is lengthy method and laborious.

• It is difficult to acquire efficiency and speed
• It may not be applicable to all topics equally well.

·         It is slow, round-about and involves trial and error. 

Synthetic Method

Synthesis means building up separate element and their combination.It proceeds from the known to the unknown facts. It is opposite of analytic.

Procedure:

Example: if  a/b=c/d, prove that ac-2b²/b=c²-2bd/d

Solution:  start from known i.e. to solve this problem we have to start from

a/b=c/d ;  subtract both side by 2b/c

and get the answer ac-2b²/b=c²-2bd/d . it is unknown

Merit Synthetic Method

• It is short method, it glorify memory, it suit the teachers and it follow the same process as given in the text book.

·          It is a method of present­ation of discovered facts.

·          It is a product of thought.

·          It is short and concise.

·          It puts together or synthesizes known facts.

·         Once forgotten, it cannot be recalled.

·          It is quick, straight forward and does without trail and error.

·          It does not satisfy doubts and questions arising in the mind of the leaner.

·          It is a special device; it is a method for the crammer.

·         It is not that easy to recall or reconstruct any forgotten step.

·          It develops memory.

·          It is informal.

·         It is simply informational.

·         There is no heuristic approach in it.

·         It is the follower of analysis.

Demerits Synthetic Method

•    It is not a psychological method.
•  There is a scope for forgetting.
• It makes the students passive listeners and encourages cramming.
• In this method confidence is generally lacking in the student.
• There is no scope of discovery.
• The recall of each step cannot be possible for every child.

Difference between Analytic Method & Synthetic Method

No.	Analytic Method	Synthetic Method
1	Analysis means breaking up into simpler elements.	Synthesis means building up separate element and their combination
2	It proceeds from the unknown to the known facts.	It proceeds from the known to the unknown facts.
3	It is a method of discovery.	It is a method of present­ation of discovered facts.
4	It is a process of thinking (exploration).	It is a product of thought.
5	It is lengthy and laborious.	It is short and concise.
6	It pulls apart or breaks up the statement under solution.	It puts together or synthesizes known facts.
7	It can be rediscovered.	Once forgotten, it cannot be recalled.
8	It is slow, round-about and involves trial and error.	It is quick, straight forward and does without trail and error.
9	It answers satisfactorily and question that may arise in the mind of pupil.	It does not satisfy doubts and questions arising in the mind of the leaner.
10	It is a general method; it is a method for the thinker and discoverer.	It is a special device; it is a method for the crammer.
11	The students can recall and reconstruct easily any step if forgotten.	It is not that easy to recall or reconstruct any forgotten step.
12	It develops originality.	It develops memory.
13	It is informal.	It is informal.
14	It is formational.	It is simply informational.
15	It is based on heuristic lines.	There is no heuristic approach in it.
16	It is fore-runner of synthetic.	It is the follower of analysis.

Conclusion: Since analysis is a lengthy method, it needs the help of Synthesis for the removal of doubts. Synthesis is the complement of the analysis method. both the method are interdependent. Teachers should offer help for the analytic form of the solution and that synthetic work should be left for the students.